Page:Scientific Memoirs, Vol. 2 (1841).djvu/237

$\cos \lambda -178\centerdot 744\sin u\sin \lambda$ , and $-925\centerdot 782R^{3}$, $-89\centerdot 024R^{3}$, $+178\centerdot 744R^{3}$ are the moments of terrestrial magnetism with respect to the axis of the earth, and to the two radii for longitudes 0 and 90. In speaking of the earth's axis, the direction towards the north pole is to be understood, and the negative sign of the corresponding moment shows that the magnetic axis makes with it an obtuse angle, or that its magnetic north pole is turned towards the south.

The direction hence found for the magnetic axis is parallel to that diameter of the earth which is from 77° 50′ north lat., and 296° 29′ lon., to 77° 50′ south lat,, 116° 29′ lon.; and the magnetic moment in relation to this axis is $=947\centerdot 08R^{3}$. It must be remembered that in our elements the unity of intensity employed is a thousandth part of the unity in common use. In order to obtain the reduction to the absolute unity established in the Intensitas Vis Magneticæ, we must remark that in that work the horizontal intensity at Göttingen for the 19th of July, 1834, was found = 1·7748, which, combined with the dip 68° 1′, gives the total intensity = 4·7414. The total intensity, according to the unity employed above, was 1357. Thus the reducing factor is = 0·0034941, and the magnetic moment of the earth, expressed according to the absolute unity,

$=3\centerdot 3092R^{3}.$

As the millimetre is the unit of length employed in the above absolute unity for the earth's magnetic force, $R$ must also be given in millimetres; and, as the ellipticity of the earth need not be taken into account, it will be sufficient to consider $R$ as the radius of a circle 40000 millions of millimetres in circumference. Hence the above magnetic moment will be expressed by a number of which the logarithm = 29,93136, or by 853800 quadrillions. By experiments made in the year 1832 (Intensitas, Art. 21) the magnetic moment of a magnet bar, of a pound weight, was found to be, according to the same absolute unity, = 100877000. The magnetic moment of the earth is therefore 8464 trillion times greater. Thus 8464 trillions of such magnet bars, with parallel magnetic axes, would be required to replace in external space the magnetic influence of the earth. Supposing the magnetism of the earth to be uniformly distributed throughout its volume, it would hence be equal to eight such bars (more exactly 7·831) for every cubic metre. This result thus enounced preserves its meaning even, if instead of